Cooperative rotating arm and straight line experiments with ITTC standard model (Mariner type ship)

ARCHIEF

PRNCTMB-648 (Rev 1-64)

Lab.

_{v. Schpsbo}

COOPERATIVE ROTATING-ARM AND STRAIGHT-LINE EXPERIMENTS WITH ITTC STANDARD

MODEL (MARINER TYPE SHIP)

Morton Gertler

The distribution of this report is unlimited

HYDROMECHANICS LABORATORY RESEARCH AND DEVELOPMENT REPORT

COOPERATIVE ROTATING-ARM AND STRAIGHTLINE EXPERIMENTS WITH ITTC STANDARD MODEL

(MARINER TYPE SHIP)

by

Morton Gertler

JUNE 1966 REPORT 2221

SR 009 01 01 Task 0102

TABLE OF CONTENTS

U

Page

ABSTRACT . 1

INTRODUCTION 1

DESCRIPTION OF MODEL AND PROTOTYPE 2

TEST APPARATUS 5

TEST PROCEDURE 8

REDUCTION AND PRESENTATION OF DATA...

DISCUSSION OF DATA.. 13

ROTATING-ARM TESTS

... 14

STRAIGHTLINE TESTS

..

20

COARISON OF THE TWO TECHNIQUES 2.5

COARISON WITH DATA OBTAINED BY OTHER

ORGANIZATIONS 28

CONCLUSIONS 33

ACKNOWLEDGMENTS. 34

REFERENCES . 34

APPENDIX A - HYDRODYNAMIC DATA OBTAINED FROM

ROTATING-ARM TESTS ... . 35

APPENDIX B - HYDRODYNAMIC DATA OBTAINED FROM

LIST OF FIGURES

Page

3

6

iii

Figure 4 - Typical Data From Rotating-Arm Tests Showing Variation

of Hydrodynamic Coefficients X', Y', and N' with Drift

Angle $ (20-Knot Condition) 16

Figure 5 - Typical Data from Rotating-Arm Tests Showing Variation

of Hydrodynamic Coefficients X', Y', and N' with Ru4der

Angle 8. (20-Knot Condition). 17

Figure 6 Typica. Data from Rotating-Arm Tests Showing Variation of Hydrodynamic Coefficients X', Y', and N' with Rudder

Angle 8R (10-Knot Condition) ...

18

Figure 7 - Typical Data From Rotating-Arm Tests Showing Variation

of Hydrodynamic Coefficients X', Y', and N' with Drift

Angle $ (10-Knot Condition) 19

Figure 8 - Typical Data from Straightline Tests Showing Variation of

Hydrodynamic Coefficients X', Y', and N' with Drift Angle

$ (20-Knot Condition) ...

21

Figure 9 - Typical Data from Straightline Tests Showing Variatjon of

Hydrodynamic Coefficients with X', Y', and N' with Rudder

Angle 8R (20-Knot Condition) - 22

Figure 10- Typical Data from Straightli.ne Tests Showing Variation of Hydrodynamic Coefficients X', Y', and N' with Drift Angle

$ (10-Knot Condition) 23

Figure 11- Typical Data from Straightline Tests Showing Variation of Hydrodynamic Coefficients X', Y', and N' with Rudder

Angle oR (10-Knot Condition) 24

Figure 1 - Lies of ITTC Standard Model (MARINER Type Ship) ...

Figure 2 - Schematic Sketch f Towing Arrangement nd Measuring

Apparatus

Figure 3 Typical Data FrOm Rotating-Arm Tests Showing Variation of Hydrodynamic Coefficients Xt, Y' and Nt with Non-dimensional Angular Velocity Component rt (20-Knot

iv

Page

Figure 12 - Roll Angle 4) and Pitch Angle B as a Function of

Drift Angle ₂₉

Figure 13 - Roll Angle and Pitch Angie 0 as a Functioz of

Angular Velocity r' 30

Figure 14 - Roll Angle + and Pitch Angle 0 as a Function of

Rudder Angle 8 31

Figure 15 - Lateral Force as a Function of Angular Velocity

for Various Drift Angles (20-Knot Condition) . 47

Figure 16 - Lateral Force as a Function of Drift Angle for

Various Angular Velocities (20-Knot Conditon) ₄₈ Figure 17 - Yawing Moment as a Function of Angular

Velocity for Various Drift Angles (20-Knot

Condition) ₄₉

Figure 18 - Yawing Moment as a Function of Drift Angle for

Various Angular Velocities (20-Knot Condition) 50

Figure 19 - Variation of Hydrodynamic Coefficients X', Yt, and N' with Propeller Advance Coefficient J (20-Knot

Condition) 51

Figure 20 - Variation of Hydrodynarnic Coefficients X', ft, and N' with Rudder Angle 8R (Without Propeller at 20-Knot

Condition) 52

Figure 21 - Lateral Force as a Function of Drift Angle for Various

Rudder Angles (20-Knot Condition) ...59

Figure 22 - Lateral Force as a, Function of Rudder Angle for Various

Drift Angles (20-Knot Condition) 60

Figure 23 - Longitudinal Force as a Function of Rudder Angle for

Various Drift Angles (20-Knot Condition) 61

Figure 24 - Yawing Moment as a Function of Drift Angle for Various

Rudder Angles (20-Knot Condition) 62

Figure 25 - Yawing Moment as a Function of Rudder Angle for Various

Page

Figure 26 - Lateral Force as a Function of Drift Angle for

Various Rudder Angles (10-Knot Condition) ...64

Figure 27 - Lateral Force asa Function of Rudder Angle for

Various Drift Angles (10-Knot Condition) 65 Figure 28 Longitudinal Force as a Function of Rudder Angle

for Various Dziit Angles (10-Knot Condition) ...66

Figure 29 - Yawing Moment as a Function of Drift Angle for

Various Rudder Angles (10-Knot Condition) 67 Figure 30 - _{Yawing Moment as a Function of Rudder Angle for}

Various Drift Angles (10-Knot Condition)

..

.

...68

Figure 31 - Effective Horsepower, Shaft Horsepowez and RPM

for MARINER. ₆₉

Figure 32 - Open Water Characteristics for MARINER Propeller. . . 70

LIST OF TABLES

Page Table 1 - Geometric Characteristics of ITTC Standard Model

and Prototype (MARINER Type Ship).. .,... .

; ...4

Table 2 - Sequence of Rotating-Arm TSts for 20-Knot Condition. _ló Table 3 _{Sequence of Str.a.ightline Tests for 20-Knot Condition}

_ii

Table 4 - Stability and Control Derivatives Determined FrOm

Rotating-Arm and Straightline Tests

Table 5 - Comparison of Hydrodynamic. Derivatives with Those

Obtained by Other Organizations ₃₂

Tble 6

Data from Rotating-Arm Tests for 20-Knot Condition ₃₆

Table 7 Data from Rotating-Arm ests for 10-Knot Condition. . _{. 41}

Table 8 Rotating-Arm Test Data for Mç4el without ropel1er

forTangeritial Speed of 20 Knots (F =

2

= 0. 259) ...45

Table 9 - Rotating-Arm Test Data for Propeller Advance Coef-ficiènt Variation for Tangential Speed of 20 Knots

(F = 0 59) and Radius of 106.79 Ft (rt = 0.2045).. ₄₆

IgL

Table 10- Data from Straightline Tests for 20-Knot Condition

(F=

J

_{= 0.259, j=}

_{= 0.979), 54}

nD

Table U - Data from Straightline Tests for 10-Knot Condition

U _{= 0 1295,}

J =

= O.979)...56

nD

vgL

N

N_r

NOTATION

The following nomenclature is in accordance. with the standards adopted by the Tenth International Towing Tank Conference September 1963.:

Symbol Dimensionless Form Definition

D Propeller diameter N N1 pL3U2

Nt-

Nr r _{- pL4U} N

N'

= pL3U N_{5R T} N5R pL3U2 = Froude number

Propeller advance coefficient

Hydrodynamic yawing mOment

Derivative of yawing moment component with respect to angtilar velocity component r

Derivative of yawing moment component with respect to linear velocity component v

Derivative of yawing moment component with. respect to rudder angle component 5R

vii

L' 1 Length of ship (in this report

length. between. perpendiculars)

n Propeller frequency of

revolu-tion

rL

U _componentYawing angular velocity

U U' = 1 Velocity of origin of body

axes relative to fluid N5

R

x

x Y 6R e viii hL2U2 Y YI= pL2U2

y=

_r OL3U Yl-V _pL2U 5R 6R _{= *pL2U2}

Coxnponent along y-axis of velocity of origin of body axes rèiátive to fluid

Hydrodynamic longitudinal

force, positive forward

Longitudinal axis, directed from after tO forward end of ship with origin at center of gravity

:Hydrodynamic lateral force, positive to starboard

Derivative of lateral fOrce component with respect to angula-r velocity component r

Derivative of lateral force component with respect to linear velocity component v

Derivative of lateral force component with respect to rudder angle. component 6R

Distance along t-ransve-rs e axi a directed tO starbOard with

origin at center of gravity

Angle of drift

Rudder angle

Pitch angle (with respect to horizontal plane)

Roll angle (with respect. to vertical plane

V Vt

U

Y

References are listed on page 34.

ABSTRACT

Pursuant to the ITTC Maneuverability Committee's Cooperative Program, the David Taylor Model Basin has carried out an extensive series of rotating-arm and straightline experiments with a 22-foot long standard model (MARINER

Type Ship). This report describes in detail the model, apparatus, and

tech-niques used in the investigation and presents the experimental results in both tabular and graphical form as nondimensional hydrodynamic coefficients and as stability and control derivatives. It is concluded that, if the same model,

instrumentation, test procedures, and initial conditions are used, the same

numerical values can be obtained for the individual static stability and control

derivatives from rotating-arm tests as from straightline tests. INTRODUCTION

The experimental investigation reported herein is part of the David Taylor Model Basin! s contribution to the ITTC Maneuverability Committee's Cooperative Program' dealing with techniques for determining the

maneu-verability characteristics of surface ships. The primary purpose of this

report is to present the data that have been obtained by means of rotating-arm and straightline tests with the ITTC Standard Model (MARINER Type Ship) along with a detailed description of the associated facilities,, instrumentation, and test techniques employed in the investigation. The data are presented in a form which should facilitate direct comparisons with similar data provided

by other participants of the Cooperative Program. The use of these data in

analog or digital computer studies to make predictions for and to establish correlations with the full-scale MARINER type ship2 will form the subject of

a future report.

The ITTC Maneuverability committee's Cooperative Program was es-tablished in 1962-63. The objective of the first phase of the program is to

establish the extent to which agreement exists between the data produced by the various laboratories using each of several alternative model test techniques.

To accomplish this objective, the Committee selected the MARINER type ship as the "Standard Model", furnished the participating laboratories with a complete

set of lines plans, and outlined the standard conditions to be adhered to in the model tests. Each organization was free to construct a model of a size compatible with its own facilities and to conduct the cooperative tests using its own instru-mentation and techniques.

The types of tests embraced by the Cooperative Program fall into two general categories called tifree -running-model" and "captive -model" tests, respectively. The term free-running-model test is applied to the well-known class of experiments in which maneuvers are performed with

dynamically-scaled models that are self-propelled without external restraint, and the

resulting motions or trajectory data are recorded. The models can be

cable-controlled, radio-cable-controlled, or manned vehicles. The term captive-model tests is used to denote the type of experiment in which the model is constrained,

usually to a towing carriage, and the forces and moments used to determine the numerical values of the hydrodynamic coefficients for the equations of

motions are measured. Included in this category are: straightline yawed-flight tests, rotating-arm tests, and planar-motion-mechanism or oscil-lation tests.

The Model Basin's participation in the Cooperative Program extends to both categories of tests. Free-running tests with a radio-controlled model have already been conducted in the Maneuvering and Seakeeping Facility using a large (about 22-foot long) model of MARINER. A separate report, containing a complete account of these tests, is being prepared and a portion of the data

has been is sued.3 In the captive-model category, the subject rotating-arm

and straightline tests were conducted with the same model and some comparative data have been issued.4 However, since the DTMB Planar-Motion-Mechanism System has not yet been adapted to test surface-ship models, the remaining part of the captive-model program will be reported separately.

This report describes the model, apparatus, and techniques used in the experiments conducted by the Model Basin for the ITTC Maneuverability Committee's Cooperative Program; outlines the procedures used in the reduction and presentation of the experimental data; discusses the quality of the data from the standpoint of scatter and repeatability; compares the rotating-arm test data with corresponding straightline test data; briefly compares the stability and control derivatives obtained from the subject tests with those obtained by some of the other participants of the Cooperative Program; and draws some conclusions concerning relative merits of the two techniques from the standpoint of determining the various hydrodynamic coefficients required for the equations of motion of surface ships.

DESCRIPTION OF MODEL AND PROTOTYPE

The MARINER Type Ship was selected for the "ITTC Standard Model" because its configuration is considered to be typical of modern commercial ships. Furthermore, extensive full-scale maneuvering data are available

for this type of ship2 making it even more desirable for the intended purpose. The configuration of the ship is shown by the lines plans given in Figure 1.

The pertinent geometrical characteristics are listed in Table 1 in terms of

model and ship dimensions.

As specified by the ITTC Maneuverability Committee, the configuration of the Standard Model is identical with that for the MARINER Type Ship described in Reference 5. However, both its displacement and trim corres-pond to the conditions thatexisted during the full-scale trials of COMPASS

ISLAND2. Thus, the configuration of the Standard Model differs from that

for which full-scale trial data are available in two respects: the bilge keels

are longer (110 feet compared with 62.5 feet) and there is no sonar dome.

AP -4 OF WAKE SURVEY Ft. 1I 20 9t 3 LBP 28-O 0 -BODY PLAN

Figure 1 - Lines of ITTC Standard Model (MARINER Type Ship)

-._

*

i

L'

....

T::L..!I

7'

I

I..

L

_{A__}

A4

a I

iM

44:

-IIPi

IIM

i L

-U] II

Th

I

/

Im,I!

auiiriii

1W4F11WII

_____ I

I

I1... ..0V I

hII.L ''

J-IL. _{/1, / -,} I.. I

I--=

I-SThTI0M PAW(, 2b-O

TABLE 1

Geometric Characteristics of ITTC Standard Model and Prototype

(MARINER 'Type Ship)

4

- Ship - Model

Hull

Length Between Perpendiculars, ft. 528.00 21.841

Beam, ft. 76.00 3.144

Mean Draft, ft. 24.50 1.013

Trim by Stern, ft. 4.00 0. 165

Displacement, tons, lbs ) 16800. 2590.0

Nominal Center of Gravity Location

Distance Aft of Station 10, ft. 6.90 0.285

Height Above Baseline, ft. 25.40 1.051

Length-Beam Ratio 6. 947 6. 947 Beam-DraftRatio 3.102 3.102 Displacement-Length Ratio 114. 13 114. 13 Prismatic CoeffIcient 0. 6246 0. 6246 Block Coefficient 0.6125 0.6125 Rudder (Semi-Balanced) Mean Chb±d, ft 13.08 0.541 Span, ft. 24.00 0.993

Total Projected Area, ft2 314. 00 0. 5373

Movable Projected Area, ft2 271.84 0.4651

AspectRatlo 1.834 1.834

Percent Balance 20.91 20.91

Rudder Area Coefficient 0. 0224 0. 0224

Maximum Design Rudder Angle, deg 40. 0 40. 0

Rudder Rate, deg/sec 2. 5 to 3. 7

-Propeller Direction of Rotation RH RH Number of Blades 4 4

Pitch, ft.

, 22.83 0.945 Diameter, ft. 22.00 0.910 Pitch-Diameter Ratio 0. 964 0. 964

Expanded Area Ratio

i1ge Eçeels

0.565 0.563

Lexigth, ft. 110.00 4.550

Depth, ft. 1;50 0.062

NOTE: fl.udder dimensions are based on immersed portion for specified displacement and trim

Ship M.ARINER

Model No. 4414

Model Propeller No. ₃₂₄₉

Linear Ratio, A 24. 175

Lines Plan Bethlehem Steel Corp. No.

Bow _{CTD C4-S-la-H15A, Alt 1}

Stern _{CTD C4-S-la-H15B, Alt 4}

Appendage Plan No.

Rudder C4-S-la-H150, Alt 4

Bilge Keels CTD-C4-S-la-H-70 and

C4-S1A-123-5 Alt III and offsets

DTMB Model 4414 was used for the entire experimental investigation covered by this report. The model is about 22 feet long, constructed of sugar pine, and painted with enamel to achieve a smooth surface finish. To fulfill the objectives of the Cooperative Program, the underwater portion of the model, including hull, propeller, rudder and bilge keels was made

geometrically similar, in every respect possible, to the Standard Model

specified by the Maneuverability Committee. The model was equipped with

an electric motor to drive the propeller and a rotary actuator to swing the

rudder. The force balances and other measuring equipment, described

later in this report, were installed in the model and supplementary lead

ballast weights were used to achieve the specified displacement and trim conditions.

TEST APPARATUS

The two major facilities that were used for the subject investigation at the David Taylor Model Basin are the Rotating-Arm Facility and the Deep-Water Towing Basin. _{The Rotating Arm Facility is described in detail in} Reference 6. It consists of a circular basin, 260 feet in diameter with a water depth of 20 feet, and a radial towing arm. The towing arm is

es-sentially a Parker truss which pivots about a bearing on a center island. It is supported at two points by virtue of the bearing at the center pivot and

the wheels on the peripheral tracks. The Deep-Water Basin, described in

Reference 7, is a conventional straightline towing basin. It has a rectangular

cross-section with a width of 52 feet and a water depth of 22 feet. The portion of the basin used for the .investigation is spanned by Towing Carriage 2 and

extends for a length of about 1780 feet.

The towing arrangement and measuring apparatus used for the experiments are shown schematically in Figure 2. To facilitate direct comparison of the two different experimental techniques, not only the model, but the towing arrangement and other equipment used for the tests in the two facilities were deliberately made identical.

The towing apparatus shown by Figure 2 was assembled from existing parts used in connection with other model tests. Since the major quantities to be determined were the hydrodynamic coefficients associated with the equations of motion defining horizontal-plane maneuvers, it was decided that the model should be held captive in those modes where forces and moments were to be measured and free to assume the appropriate underwater con-figuration in the remaining modes. This was accomplished by arranging the towing apparatus so that the model is restrained in yaw, sidesway, and surge

but is free to pitch, heave, and roll. As indicated by the sketch, the

pin-joints in combination with the gimbals on the towing linkages allow the model

to both pitch and heave. The gimbals, which are associated with the gage system, permit movement in three degrees of freedom about their own individual axes. However, collectively they provide restraint in yaw, sidesway and surge, but allow movement in roll since their longitudinal axes are coincident. The

model can be locked out in roll, if desired, by inserting a locking pin into the roll balance contained in one of the gimbals.

a'

AP

P

Tow Bracket

Gimbal Bearing or Roll Balance

Enlarged View of a Gage Assembly

21.841

Figure 2 - Schematic Sketch of Towing Arrangement and 'Measuring Apparatus (All dimensions are in feet)

.-T:i,JJJr,/,,',

-1 3.0 Gimbal. CG-1.q51 _Midships Yaw Table pin '- 0.285 Gimbal

The gage system and associated recording equipment is described in detail in Reference 8. It is essentially the same as that used with the DTMB Planar-Motion-Mechanism System. As seen in the enlarged view of Figure 2, each gage assembly consists of three modular force gages, connected in

series and oriented to measure X-, Y-, and Z-forces together with either

a gimbal or roll balance. Since the model is free to pitch and heave in the

subje,ct experiments, the Z-gage is used merely as a spacer. Also, the

roll balance is inactive because the locking pin is removed and the model

is free to roll. One end of each gage assembly.is attached to the model by:

means of a baseplate; the other end is attached to the yaw table through the tow bracket. Thus, the total weight of all of the components of the gage.' system, up to and including about half the horizontal member of each towing linkage, becomes part of the model ballast.

The gage assemblies are located in the model so that they measure components of force referred to a body-axis system having as its origin the. center of gravity of the ship (see Table 1). The gimbal centers are spaced equidistant (±3. 0 feet) from either side of the reference point; the gages sense pure reaction forces at each gimbal center and the moment about these

gimbal centers is zero. It should be mentioned that the individual gages do

not sense the portion of the inertial forces due to the weight of the parts of the system between the center of the gage and the center of the horizontal member of the towing linkage. These weights have been calculated and

confirmed experimentally to be 131 5 pounds and 181 0 pounds up to the centers of the pair of Y-gages and the pair of X-gages., respectively. In each case, the weight involved amounts to roughly 5 percent of the model displacement.

Therefore, it is necessary to make appropriate corrections to the measured X and Y forces, as explained in a later section of this report.

The. devices for setting and reading out the various angles are not shown

by the sketch inFigure 2. 'The rudder angles can be set and read out remotely

on the towing carriage by means of an electric rotary actuator which contains a potentiometer which is calibrated over a range of ±45 degrees. The yaw (drift) angles are set by rotating the model-yaw table combination, about a central bearing, with respect to the towing carriage.. Somewhat different

arrangements are used for this purpose on the two facilities. On Carriage 2,

the yaw angles are set manually by inserting a positioning pin and heavy bolt into previously indexed holes in plates between the yaw table and towing

carriage. On the Rotating Arm, the yaw table is motor-driven by, and

operates in parallel with the angle-positioning device permanently installed on the facility. 6 _{The angles are sensed on this device by a mechanical}

read-out digital counter installed at the motor end of the gear train. Thus, 'the yaw angles can be both set and read out at the instrument console on the

-Rotating Arm. The pitch and roll angles assumed by the model during the course of the experiments on both facilities are sensed and read out bya Minneapolis Honey-well Vertical Gyroscope. The propeller rpm' is sensed and read out by means of a tachometer generator.

On the Rotating Arm, the radius settings are made by means of the sub-carriage which Is moved radially along a pair of rails by a windlass and cable. _{The precise setting is obtained manually by inserting four}

1-inch-diameter pins, one at each of the four corners of the sub-carriage, into index

holes on the rail. The pins also serve as strength members to hold the

car-riage in place.

The measurements obtained with the foregoing instrumentation are recorded

during the tests by means of the digital recording system described in detail in Reference 8. The recording equipment is located in the InStrument Pent-house in the case of Carriage 2 and at an instrument console in the case of the Rotating Arm.

TEST PROCEDURE

Prior to conducting a given series of tests for the formal program, the

model was carefully ballasted and trimmed as follows:

The fully ballasted model (including all instrumentation and equipment contributing to its weight) was first weighed on a platform scale. While weighing, the towing linkages and electric cables were supported so that the model weight (or displacement) was precisely the same as it would be when attached to the towing carriage. The model was then put into the water and the ballast weights were moved longitudinally to obtain the correct trim, as indicated

by draft marks; transversely toobtain zero heel, as indicated by a level placed

across the top lift of the model; and vertically to obtain the correct height for

the center of gravity, as indicated by moment-to-trim tests Insofar as could

be determined, the resulting conditions for the model at rest in the water were identical to those listed in Table 1. Since captive-model tests of the steady-state variety were to be conducted, no attempt was made to swing the model to obtain the radii of gyration.

In addition, all of the measuring instruments were carefully calibrated

prior to the tests. The modular force gages were individually calibrated

with standardized weights; the vertical gyroscope was calibrated in roll and

pitch on a tilt table, the rudder angle sensor was calibrated by setting the

rudder at discrete angles (as indicated by a protractor) with respect to

acenter-line scribed on the model; and the tachometer generator used to measure propeller rpm was calibrated with a synchronous motor.

The general procedure used for the fortha.l tests in the two facilities

ae

as follows:

With the model attached to the towing carriage and at rest, the digital

recorders are balanced and adjusted to read zero for zero force on the

modu-lar gagesand zero angles on the vertical gyroscope, rudder, and yaw table

(RQtating Arm only). _{Then, for any given model setting of yaw angle, rudder}

angle, and turning radius, the model is brought up to a predetermined speed

cOrresponding on Froude scaling to the full-scale approach speed. At the. same time, the propeller speed is ad,justed to an rpm corresponding to the point of propulsion of the full-scale ship for the given speed When essentially steady cOnditions are reached, as indicated by the readings on the digital recorder, the. run is maintained for at least 10 seconds. The recorder is then put on "hOld" and the readings which represent _{average steady-state values are}

transferred to the data sheet by an automatic typewriter.8 _{At the end of a run}

or serie.s of runs, the model is towed slowly back to the starting position in the basin. A waiting period of at least 12 minutes duration _{between the} begin-ning of successive runs is taken to allow the water in the basin to become free of waves and currents.

The rotating-arm tests were _{run at approach speeds (tangential velocities)}

of 4. 06 and 2. 03 knots corresponding to 20 and 10 _{knots full-scale, respectively..}

At each speed, the propeller rpm _{was adjusted to correspond to the specified.}

point of propulsion (for full-scale ship proceeding on straight course). The

rpm was based on the results of propulsion tests conducted on the same

MARINER model rather than that presented for COMPASS ISLAND in Reference

2. _{To avoid operating in a current generated by the wake of the model, each}

run was completed within one revolution of the Rotating Arm, consequently, it was not practical to attempt to obtain reliable measurements for more than one model setting.during any one run.

The most complete set of tests on the Rotating Arm was carried out for the 20-knot condition. _{The sequence of tests for this condition, is summarized} by Table 2.

In each group of tests listed in Table 2, two of the parameters were held constant while the third was varied in discrete increments over the range shown. Groups JR, ZR, and 3R are considered to be _{reference tests.} They were designed to permit as direct determination of the stability and

_control

derivatives

,

N ', Y

" yr" and Nr' as possible with a facility of this type, and also'1to erxble drrect comparisons to be made with similar quantities obtained in other facilities or by other techniques. _{The value of} r' = 0. 2045 used in the reference tests of Groups 1R and 2R _{was based on the} largest radius that could be obtained in the Rotating Arm Facility _{with the} subject model without incurring wall effects. It was hoped that this radius would be large enough to approximate the straightline case (r' = 0) from the standpoint of directly determining static stability and control derivatives from the slopes of the Y' and N' versus a-curves and the Yt and N1 versus 8R -curves.

The tests in Group 3R were designed to permit direct determination of the

derivatives Y' and N'. The remaining

_{groups of rotating-arm tests were}

designed to reveal nonlinearities and coupling effects. _{In addition to the groups.} of tests shown in Table 2, a special group of tests was conducted on the model without propeller for a condition of r' = 0. 2045, 0, with O varied between

0 and -35. 0 degrees. Also, a few runs _{were made for a condition of r' = 0. 2045,}

80, and ô

= 0 with propeller rpm varied to give advanced coefficients J of. from 0.652 to 3.931; and for a condition r' 0.2045, 3 0, and O 35deg for values of J of from 0.652 to 0. 979.

TABLE 2

Sequence of Rotating-Arm Tests for 20-Knot _condition

10 Group No.

_r'

degrees _degrees 1R _{0.2045 -5.0 to 18.0} 0 ZR _{0.2045 0 5.0 to -35.0} 3R _{0. 1858 to 0.7757 0 0} 4R _{0.6246 -5.Oto 20.0 0} 5R 0. 6246 0 -5. 0 to -35.0 6R 0. 6246 10. 0 _{-5. 0 to -35. 0} 7R _{0.6246 20 -5.Oto-35.,O} 8R _{0.2930 -5. 0 to 20. 0 0} 9R _{0. 2930 10.0 0 to -35.0} JOR _{0.2930 20.0}

_{0th -35.0}

hR

0.2045 0 -10.0 to -35. Q 1.ZR _{0.2045 10.Q 0}

_{to -35.0}

13R _{0.2045 20.0}

_{0 to -35.0}

The straightline tests were run at the same approach speeds and propeller

rpms as used for the rotating-arm tests. However, due to the length of the

straightline basin, it was possible to make from four to six steady-state runs

in one complete trip up the basin. Since only the rudder setting was remotely adjustable, the yaw angle setting was made while the model was stationary and the incremental rudder-angle settings were made while the modeiwas proceeding at constant approach speed The sequence of straightline tests conducted for the.. 20-knot condition is summarized by Table 3.

TABLE 3

Sequence of Straightline Tests for 20-Knot. Condition

Group iS was conducted as a reference test to permit direct determination of the control derivatives and N8. Because of the lack of a remotely

adjustable yaw-table, it was considered too time.- consuming to make a reference

test for the static stability derivatives Y'and Nv' Consequently, it is necessary

to obtain these derivatives from the cross-plots of the data obtained from Grpups iS through 6S for the case of 6R = 0.

REDUCTION AND PRESENTATION OF DATA

The methods used to reduce the data for the Cooperative Program are considered to be reasonably representative of current practices followed at the David Taylor Model Basin in connection with captive-model stability and

control tests for surface ships. The procedural steps are as follows:

1 The Y-forces measured, as reactions at the gimbal centers by each of

two of the modular gages are added vectorially to obtain the total mo4el Y-force. 11 Group No. -4egrees degreesÔR iS 0

20.Oto-35.0

2S . 5

Oto-35.0

3S 10

Oto-35.0

4S 15 Oto-35.,0 .5S . . . -.6.4 0 to -35..0 6S -10

Oto-35.0

The same two Y-forces are subtracted vectorially and the vector difference is multiplied by the longitudinal distance from one gimbal

center to the reference point (CG) to obtain the model N-moment. The X-forces indicated by each of the other two modular gages are added vectorially to give the total X-force.

The values of the measured model X-force, Y-force, and N-moment are converted to nondimensional coefficients in accordance with the ITTC Standard Nomenclature given in this report.

The force coefficients based on the gage readings are "corrected" to

account for instrumentation tare and, in the case of the rotating-arm

data, for centrifugal force to obtain the hydrodynamic coefficients X' and Y'. No correction is required for the hydrodynamic yawing moment coefficient N' since the reference point is at the model center of gravity.

The instrumentation tare mentioned in Step 5 results from that portion of the model weight which is not sensed by a given pair of modular gages (see

section on Test Apparatus) It is affected both by the angles (roll and pitch) assumed by the model while underway and the centrifugal force exerted on the model during rotating-arm tests. In addition to correcting for its effect on the tare, the usual practice at the Taylor Model Basin is to exclude the centrifugal force entirely when presenting hydrodynamic force coefficients.

In accordance with the foregoing, the corrections made to the force coef-fic-lents based on the direct gage readings to obtain the hydrodynamic force coefficients Y' and X' are given by the following expressions

= GR

+ m. sin

+ (m' - my') r' cos f3 cos cb

= GR + 0. 000405 sin + (0. 007978 - 0. 000405) r' cos $ cos

= GR + 0.000405 sin + 0.007573 r' cos cos and

X' = XGR' - m sin e + (m' - m ') r' sin$ cos 9, or neglecting the

effect of 9 since its maximum value is degree, = XGR' + (m' - mX)

r' sin

= XGR' + (0. 007978 - 0.000557) r' sin. = XGR' + 0.007421

r' sin $

where

GR' is the Y-force coefficient based_{readings on the two Y-gages.,} 'GR is the X-force coefficient based

is the mass coefficient based on ment of the model,

readings on the two X-gages

is the mass coefficient based on not sensed by the Y-gages, and rn is the mass coefficient based on

not sensed by the X-gages

on the summation of the direct

on the summation of the direct

the total weight or

displace-the portion of displace-the model weight

the portion of the model weight

To enable independent analysis, the numerical values of the hydrodynami.c coefficients' X', Y', and, N' obtained by the foregoing reduction process are presented in the appendixes both as tables of individual data points and as cross-curves showing the functional relationship between these hydrodynamic coefficients and the kinematic variables r', 8 Appendix A contains the

data obtained from the rotating-arm tests for the 20-knot and 10-knot conditions and Appendix B contains the data obtained from the straightline tests at the same two conditions Included in Appendix B are the results of propulsion tests of the MARINER model conducted at approximately standard conditions and the results of open-water tests of the model propeller used in all of the experiments.

In the body, of the report, fàired curves of X', Y', and Nt and associated

data. points, separately expressed as functions of 8, r', and 6R' are presented for the so-called reference coaditions. These curves are plotted on a scale

which is intended to be large enough to permit quantitative determination of stability and control derivatives, to accentuate the degree of scatter among data points; and to indicate' trends such as the existence of nonlinearities. In addition, the free motions (roll angles and pitch angles) recorded during

the tests are presented as faired curves in which the angles a-re separately expressed as functions of f3,

r', and 6

The stability and control derivatives

determined from the reference curves, and in some cases from the

cross-curves in the appendixes, are presented in the form of tables which compare the numerical values obtained either by different test techniques or by different

laboratories.

DISCUSSION OF DATA

As mentioned in the Introduction, the subject investigation is concrned primarily with experimental techniques. Accordingly, in the discussion that

follows, the emphasis is placed On accuracy, repeatability, trends, and other

factors pertinent to the technique, rather than to the significance of the data in regard to quality of design and expected' performance of the specific ship. The

data obtained from each of the two types of captive-model tests are first ths-cussed independently and then the two techniques are compared on basis of numerical values obtained for certain stability and control derivatives ROTATING-ARM TESTS

Typical data obtained frO the rotating-arm tests are shown by the reference

curves presented in Figures 3, 4, and 5 for the 20-knot condition and in Figures 6 and 7 for the 10-knot condition.

Figure 3 shows the variation of the hydrodynarnic coefficients X', Y', and N' with the nondimensional angular velocity component r' for the 20-knot condition, as derived from Test Group 3R (Table 2). In general, the data points for each of these hydrodynamic coefficients follow a smooth faired curve over the entire range investigated The small amount of scatter shown around r' = 0 2045 in

each case, is a measure of repeatability since three of the four data points

were obtained from other groups of tests. Two of these groups of tests involved changes in either yaw-angle setting or rudder-angle setting. It is very difficult

to restore the model to identically the same initial settings, especially where

these settings are zero, after such changes have been made. It is considered, therefore, that the small amount of scatter shown constitutes good repeatability.

It is interesting to note that the Y'-curve is nearly linear up to an r' of about

0.4 and that the Nt_curve is nearly linear up to an r' of about 0 3.

Charac-teristically, the X' curve is nonlinear, but the change in X',with constant

propeller rpm, is very small over a wide range of r'. The range of r' covered

in the experiments is in excess of that attained by the full-scale ship2 (r' of about 0. 6).

Figure 4 shows the variation of the hydrOdynamic coefficients X', Y, and N' with 8, as derived from Test Group 1R. The points for this variation also fall on reasonably faired curve,s and exhibit very little scatter. The amount

of scatter shown at 13 = 0 is, of course, equivalent to that shown in Figure 3

at r' = 0 2045 The Y'-curve is nearly linear up to a 8 of about 7 degrees

However, the N'-curve , as well as the X'-curve, tends to be nonlinear over

the entire range of 8-values. It should be understood, however, that the range

of 13 - values covered by the experiments is greatly in excess of the maximum steady that can be attained by the full-scale ship which was shown to be about 13 degrees2.

'igure 5 shows the variation of the hydrodynamic coefficients X', Y', and N' with 6R' as derived from Test, Group ZR. In addition to the scatter about

= 0, which is equivalent to that shown about r' 0. 2045 and = 0 in Figures 3

and 4, respectively, there is scatter in the Y'- and N'- data over a range of óRfrom

0 to 15 degrees It is believed that this could be due, for most part, to lost

motion between the rudderstock and the angle sensor located in the actuator. An attempt to overcome this type of lost motion was made by installing a spring in the. actuator system prior to conducting the experiments. Nevertheless, the data indicate that there may have been lost motion amounting to as much as 1

-0. 2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 -2 0 -2.2 -2.4 -2.6 103x -2.8

(=O;oR0)

IkI.iiiiiniiiu

llhIIiiIiiiIU"I

UIiI!iiIlllIllllI

-In"

1111111

IIllI

Figure 3 - Typical Data from Rotating-Arm Tests Showing Variation of

Hydrodynamic Coefficients X', Y' and N' with Nondimensional Angular Velocity Component r' (20-Knot Condition)

- 15 2 8 x 2.4 20 16 C 12 a 0 U a U 0 0.8 t a I. a a 04 C a U 0 0 LI a U I, 0 04 C 0 0 C 0 08 -1.2 -1.6 -2.0 2.4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. 8 0.9 Nondirnenaional Angular Velocity Component r

Os 103x 1.6 z

iI

0 -1.2 0 0. ZO45) N' YI 8 -3 x 10 6 4 S "4 U "4 0 U S U '4 0 6

Figure 4 - Typical Data from Rotating-Arm Tests Showing Variation of Hydrodynamic Coefficients

X', Y', and' N' with Drift Angle (20-Knot .Condition)

0 2 4 '4 S XI 0 0 0; = 12.0 14.0 16. 0 18 0 20.0 2.0 4.0 6.0 8.0 10.0

103x 1.2 4) U 0.8 41 0 U 4) U 0 0.4 4) 14 -1

30

-w U -I -0.4 U 4) U I. 0 -0.8 4.. 44 0 -1.2 = 0; r' = 0. 1045) R - XI Yl 0 -36

Figure 5 - Typical. Data from Rotating-Arm Tests Showing Variation of Hydrodynamic Coefficients X', Y',, and N' with Rudder Angle 6R (20-Knot Condition)

0 6 x io 0.4 0.2 0 -0.2 0.4 -0.6 -8 -4 0 4 -32 -28 -24 -20 -16 -12

Rudder Angle 6 in degree a

4-0.8 14 0.4 k 4 -0 4-U ' -04 0

0

U 0 -0.8, 4-"4 0 -= 0; r' -=0.2045) 0 0 N' -36

Figure 6 - Typical Data from Rotating-Arm Tests Showing Variation of Hydrodynamic Coefficients X', Y', and N' with Rudder Angle 6 (10-Knot Condition)

0.6 x 0.4 z 0.4 E -0. 2 -8 -4 0 -12 -24 -20

Rudder Angle 6 in degrees

R

-28 -32

103x U I, 0 o 0 E U 0 o -0.4 U 0 r. L0.8 0 0 a XI 0 0

Figure 7 - Typical Data from Rotating-Arm Tests Showing Variation of Hydrodynamic Coefficients X', Y', and N' with Drift Angle (10-Knot Condition)

2 1.6 1.2 0.8 0.4 0 8x 1O (8 R = 0; r 0.2045) 6 U S 0 0 U I_I. S I.' Yl 12 14 16 18 20 -4 -2 0 2 4 6 8 10

degree. Since the experiments were conducted, the Model Basin has developed a new device that accurately senses the angle at the ruddérstock, which should correct this difficulty in future experiments of' this kind, The figure shows

that the Y'- and N'-curves are nearly linear over a range of 6R values from 0

to at least 12 degrees.

As mentioned previously, the rotating-arm tests conducted for the 10-knot condition were comparatively incomplete. However., some observations can be made on basis of the data presented in Figures 6 and 7. The variation of the hydrodynamic coefficients X', Yt, and NT with 6R is shown by Figure 6.

In comparison with Figure 5, there appears to be considerably more scatter

for the 10-knot condition than for the 20-knot condition. This would normally be expected since the forces being measured with the same instrumentation for the 10-knot condition are about one-fourth the magnitude of the comparable forces for the 20-knot condition. In spite of this, however, there appears to

be very little scatter in the data for the a-variation shown in Figure 7. The

scatter in Figure 6 may be explained, at least in part, by the erratic flow

conditions in the vicinity of the rudder resulting from the relatively low Reynolds numbers for the 10-knot cOndition.

All in all, the data from the rotating-arm tests appear to be reasonably accurate, consistent, and repeatable on a day today basis. Some

improve-ment can be expected in the future when towing apparatus and other equipimprove-ment which is specifically designed for captive-model testing of surface-ship models

on the Rotating Arm Facility becomes available. STRAIGHTLINE TESTS

Typical data obtained from the straightline tests are shown by Figures 8

and 9 for the 20-knot condition and by Figures 10 and ii for the 10-knot _condition. As mentioned previously, only the 8R -variation (Group iS in Table 3) can be

considered truly as a reference test since it involves changing only one para-meter (oR) while the other() remains unchanged throughout the _{group of runs.}

Figure. 9 shows that, for the 20-knot condition, the data f-rom the reference

test define a faired curve with very little scatter. The small spread between

the pairs of data points at any given rudder setting is due to the fact that the data are obtained from two separate sets of runs. To this extent, this spread

is indicative of the repeatability of the data. Figure ii shows equally good

results for the 10-knot condition insofar as scatter of data is concerned. Figures

9 and 11 both show that the Y'- and Nt_curves are nearly linear over a range of 8R values of from 0 to at least 12 degrees, as was.the case for the

rotating-arm tests.

The data points for the $-variation (Figures 8 and 10) also appear to fall on smooth faired curves with very little scatter. It would have been desirable,

however, if the $-variation had been performedas a reference test with 8

varied in 1 or 2-degree increments between 0 and 10 degrees This would have permitted a more precise delineation of the t_ and N'-curves which, in turn,

103x i.z 1.0 0.8 U 0.6 0.4 0.2 C 0

I

C C bO C o

-.

-0.8 (ÔR= 0) 0 N' Yl XI -12 -10 -8 -6 -4 -2 0 2 4 6

Drift Angle $ in degrees

Figure 8 - Typical Data from Straightline Tests Showing Variation of Hydrodynamic Coefficients X', Y', and N' with Drift Angle (Z0Knot Condition)

18 6 x 10 S 4 3 2 0 -2 -3 -4 8 10 12 14 16

l03x 0.8 z e 0. U S 0 0 0.4 S 0 0.2 Cs . °:

j

-0.8

H

0) N'

Figure 9 Typical Data from Straightline Tests Showing Variation of Hydrody-namic Coefficients X', Y', and Nt with Rudder Angle 8R (Z0-Knot Condition).

4 x 10 3 2 1 S 0 0 Os_U I. 0 I. I s Cs -2 3 -4 12 16 20 -36 -32 -28 -24 -20 -16 -li -8 -4

IIIIi'iii!i1iiij!111111

0.6

1IIIIIIIII

1,aaaIIIIII

i°.

4IIIIIIIIiIiiiIiimaIahhh11h111hhh1

_{aaaaaaaaaa"1a11111}

0.21111111

II!!m4h111

6I4IijiiiaIIjI1111hhI1

-12 -10 6 - 4 2 0' 6 l0 12 14 16 18 20 22

Drift Angle 3 in degrees

Figure 10 - Typical Data from Straight1iIe TeStB Showing Variatiofl of HydrodY Coefficients

x', Y', and N' with Drift Angle fi (10-Knot Condition)

1.4

-0. 1 0.4 -0.8 0 Yli N'

Figure 11 - Typical Data from Stráightiine Tests Showing Variation of Hydrodynamic Coefficients

X', Y', and N' with Rudder, Angle ÔR(lO_Knot Condition)

0. 2 103x 1.0 0.8 441 U 0.6 4, 0 0 0 4, E 0.4 41) 0 414 0 4) U '41-41 41) 0 0 4, U 0 I -0.6 0 5 x 10 4 3 2 0 1 2 3 4 -36 -32 -28 -24 -20 -16 -12 -8 -4 0

Rudder Angle 6 in degrees

R

would have enabled a more accurate determination of the static derivatives Y

v

and N_v

In spite of the way that the tests for the 8-variation were conducted, the data from the straight-line tests appear to be reasonably accurate, consistent, and repeatable.

COMPARISON OF THE TWO TECHNIQUES

The data obtained from the rotating-arm and straightline tests are compared in Table 4 on the basis of stability and control derivatives. The most direct comparison that can be made between the two technique,s is with the derivatives

Y and N6R . This is because, in the subject experiments, r' had very little

irt1uence on these two derivatives. For example, the derivatives read off the

-Y' and N' versus 8R -curves for the cases of R' = 0. 2045 and R' = 0. 2930 had essentially the same values. Consequently, it was assumed that no extrapola-tion to r' = 0 was required. It may be seen from Table 4 that the values of

Y' and NR' obtained from the rotating-arm tests agree with the corresponding

values froni the straightline tests within 4 percent for the 20-knot condition;

the values from the two techniques agree almost exact-ly for the 10-knot condition. This demonstrates that if the same model, the same instrumentation, and the

same test procedures are used, it is possible to obtain essentially the same

values for the two rudder derivatives from tests in the two facilities. It should be noted that, within the accuracy of the experiments, the results of both the

rotating-arm tests and straightline tests indicate that the values for both

and NoR' do not- change in going from the 20-knot to the 10-knot condition. The precise agreement shOwn by Table 4 in the values of and N obtained by the two techniques must be considered as fortuitous. The vValuès

listed for the straightline tests are considered to be reliable since they are obtained by means of a direct process. On the other hand, the values listed

for the rotating-arm tests were obtained by extrapolating the appropriate cross-curves given in Appendix A to the case of r' 0. As mentioned previously, the reference value r' = 0. 2045 was selected with the hope that the slopes of the Y'- and N' versus 8-curves at 8= 0 would approach those for the straightline

case. This turned out on the subject tests to be a reasonably good assumption

for Y ', but not for N '.

For example, the values of Y ' and.N ' read from

the rference curves t'r'

0. 2045) for the 20-knot condiion areV17.. 48 x io

and 3. 065 x i0 compared,respectively,with 16. 90 x i0 and 4. 469 x 10 shown for the straightline case in Table 4.. Thus it appears that there is a fairly strong

coupling effect of r' on 8 as far as the yawing moment coefficient is concerned even at small values of r' and 8. It should be ioted from Table 4 that the values for the derivatives Y ' and N ' for the 20-knot condition differ

con-siderably from those for theS10kno1Ycondition.

TABLE 4

Stability and Control Derivatives Determined From Rotating-Arm and Straightline Tests

(Valuec inuatbe multiplied by 1O3)

20-Knot Condition 10-Knot Condition

20-Knot CondItion

Without Propeller

Derivative Rotating - Arm Str aightilne Rotating - Arm Str aightline Rotating - Arm

y

-16.0

-16.90 - -13.29 -V N ' v -4.47 -4.47 - -3.51 -y t ôr 2.87 2.98 2.861 2.87 1.47 N ' or -1.38 -1.43 -1.374 -1.38 -0.71

y'

_r 2.62 - - -

-N '

_r -2.30 - - -

-NOTE: All values except those for the case without propellers correspond to the point

H of propulsion for the full-scale ship which is taken to be at a propeller advance

J - 0. 979. All

coefficient derivatives listed for the Rotating-Arm

The values giyen in Table 4 for the rotary derivatives Y ' and N are

considered to be reliable since they are obtained directly frSm the rresults of

a properly conducted rotating-arm reference test. Since rotary derivatives

cannot be obtained from a simple straightline. test , it is planned for the

future to conduct tests in the straightline basin with a planar motion mechanism using the same model and measuring equipment. This should provide rotary derivatives from an alternative technique which can be compared with those in Table 4.

For the case of 8 = r' = = 0, the lateral force and yawing moment on

a single-screw ship are not zero but usually have some finite value. These are usually denoted in nondiniensional form as the coefficients Y,' and Nt'.

The effects of these coefficients are manifested on the actual ship by dif-ferences between the steady-turning diameters obtained from right and left

turns ,conducted at equal rudder angles. Furthermore, the rud4er setting

required for equilibrium straightline flight (neutral angle) is some value other than zero. It is extremely ifficult to obtain reliable numerical values for these coefficients from model tests without resorting to special procedures.

Among, the two techniques, the straightline test offers the best possibilities for accurately determining Y

_{and N' since, at least in the ideal sense, it}

is possible to set the model at a condition of = r' = = 0. In practice, how-ever, due to problems in alignment and asymmetries in the model itself, it is difficult to separate out the effect due to the propeller alone. It was intended

to conduct a special group of straightline tejts using first a right-hand

pro-peller, then a dummy hub, and then a left-hand propeller. This would have provided data which could be used to directly determine the desired value of

and N' since it would eliminate the effects of uncertainties in settings

of _{and 6R as well as the effects of other asymmetries in the model or towing}

system. Unlortunately, these tests were not conducted due to limitations in time. Consequently, the values of Y' and N' shown, for example, 'in Figure 8

are considered to be neither representative of the full scale nor even consistent in sign with each other.

It is even more difficult to obtain accurate values'of Y' and N' from rotating-arm tests since an extrapolation on rt is required to obtain a case of B r' = = 0. One technique that has been suggested is to rotate the model

180 degrees about the reference point to obtain a range of negative values of

rt so that an interpolation, rather thanan extrapolation, could be made to the

case of = r' = = 0. This procedure is not considered to be practical for

two reasons: first, it is difficult to preserve the initial alignment at the largest

radius after swinging the rriodel around by 180 degrees and, secondly, there is no guarantee that Y' and Nt will be linear between the plus and minus values

of r' corresponding to the largest radius.

The previous discussion is concerned primarily with _{an evaluation of the} two different techniques from the standpoint of determining derivatives for

linearized equations of motion. It is apparent that, between these two techniques,

the straightline test is the more accurate means for determining the derivatives

N and NAR and the rotating arm test is required for determining

and' N '. _{The str'.ightline test is the more direct procedure for determining} noniineariies caused solely by 8 and 6R variations. The rotating arm is the

more direct procedure for determining nonlinearities caused solely by the r' variation. For determining coupling effects, the two techniques complement each other. _{The straightline test .is the more direct procedure for determining}

arid N' for single-screw ships, but even here a special technique must be

employed to obtain reliable results.

The separate effects of the kinematic variables

rt, and

8R on the free motions of the ship are shown by Figures 12, 13, and 14. In all cases, the

change in pitch angle e is small, amounting to at most 0. 6 degree _{at the 20-knot} condition. - The roll angle variation with r' and 8R is also small. However, the variation with $ is significantly larger, amounting to as much as -6. 0 degrees at $ = 13 degrees for the 20-knot condition. However, this value of is

associ-ated with the tightest turn that the ship can make, and the speed in the turn will be considerably less than the approach speed. Consequently, the largest roll angle that would occur in the real case would probably be no more than -3. 0 degrees.

COMPARISON WITH DATA OBTAINED BY OTHER ORGANIZATIONS

Reference 3 summarizes the status and results of the ITTC "Standard Captive-Model Tests" conducted by the varjous member organizations and repprted prior to May 1966. Included are detailed comparisons made both on

the basis of stability and control derivatives and on the basis of faired curves showing the variations of the hydrodynamic coefficients X', Y', and N' _with the kinematic variables 8, r', and 8R Such a comparison and the attendant implications are considered to be beyond the scope of this report. Neverthe-less, it is of interest to compare those stability and control derivatives _obtained

in the subject investigation with corresponding derivatives obtained _{by other} facilities and techniques. Accordingly, the pertinent derivatives are compared in Table 5. _{In all cases, the derivatives correspond to the standard condition} closest to the 20-knot condition that was investigated by the particular

organization.

It may be seen from Table 5 that, although the values produced by the David Taylor Model Basin on the two different facilities are in close agreement, there

is a wide disparity between these values and the corresponding values produced by the other organizations. Some of these differences can be attributed to a variety of factors noted in Reference 3 such as the effects of: model size, basin

size, the type of towing arrangement used (for example whether or not the model was free to trim), omission of appendages such as bilge keels, operating

\Pcnglee

gle $ 4 8 12 16 20 -12 -8 -4 0 4 8

Drift Angle in degrees

Figure 12 - Roll Angle + and Pitch Angie U as a Function of Drift Angie

Pitch Angle 0

Roll Angle

0.1 0.2 0 3 0.4 0.5 0.6 Nondimensional Angular Velocity Component r'

0.7 0.8 Figure 13 - Roll Angle$ and Pitch Angle 8 as a Function of Angular Velocity r'

(Solid line denotes 20-knot condition; broken line denotes 10-knot condition)

-4

'-4

-1

-35 -30 -25 -20 -15 -10 -5

Rudder Angle 6 in degrees

Figure 14 - Roll Angie $ and Pitch Angle 6 as a Function of Rudder Angie 8R (Solid line denotes 20_knot condition;. broken line denotes 10-knot condition)

TABLE 5

Comparison of Hydrodynamic Derivatives with ThOse Obtained by Other Organizations

(Values listed are for the standard conthtion closest

to the 20-knot condition. The values must be multiplied by 10 3)

32

Organization Type of Test 'v Y N6 Nr'

David Taylor Straightline -16 90 -4 47 2 98 -1 43

Model Basin, RotatingArm -16.90 -4.47 2.87 -1. 38 2.62 -2. 30

USA University of Straightline -11.80 -3.80 California, USA Planar-Motion Mechanistn -13.30 -3.80 2. 60 -2. 10

Hydro- and Straightline -11.60 -2.91 2.18 -1.33

Aero-dynamics Planar-MOtionMechanism

1aboratory,

Denmark 272 -1.91

Techno-logical Planar-MotionMechanism -10.10 -3.49

22

2.90 -2.00

University Deift, Holland Nagasaki Straightline -12.41 -4.58 Technical Institute

NOTE: For further particulars such as model size, basin dimensions, towing arrangement, appendages, etc. See Reference 4.

at model instead of ship point of propulsion, etc. Unfortunately, the resolution of these differences will have to remain for some future time when sufficient information is available to properly assess how the foregoing factors affect the numerical values of the stability and control derivatives.

CONCLUSIONS

On basis of rotating.arm and straightline experiments with a 22-foot long standard model (MARINER Type Ship) conducted at the David Taylor Model Basin for the ITTC Maneuverability Committee's Cooperative Program, the following conclusions are drawn:

If the model, instrumentation, test procedures, initial test conditions,

and approach speed are kept the same, it is possible to obtain the same

numerical values for the individual derivatives Y ', N ', ', and N5 ' in the

Rotating Arm Facility as in the Straightline Basii'(FacIity. R

Among the two test techniques investigated. the straightline type of test is an inherently more direct and accurate method for determining the static

stability and control derivatives tv" Ny', _R' and NoR', and the nonlinearities

in the force and moment coefficients Y' and ' caused solely by variations in either $ or 6R

Among the two test techniques investigated, the rotating-arm type of test i. an itiherently accurate technique for determining the rotary derivatives Y ' and Nr'; and the nonliriearities in Y' and N1 caused solely by the r' variation.

Te rotary derivatives cannot be obtained by a simple straightline test, but

require a planar motion mechanism or other equivalent device.

The two techniques complement each other when it comes to determining coupling effects in the hydrodynamic coef-ficients.

5 For single-screw ships, a special technique utilizing straighthne tests

is required to accurately determine the coefficients Y' and N' which result

from an interation between the propelle,r and stern of the ship while on straight course.

6. In going from the 2O-knot to the 10-knot condition, the values of the

control derivatives Y' and NOR' do not change significantly but there is a

substantial change in The values of the static stability derivatives '' and Ny'.

Sufficient data were not obtained for the 10-knot condition to determine whether the values of the rotary derivatives Yr'and Nr' change significantly with approach

speed..

ACK NOW LEDGME NTS

The author is grateful to those members of the Stability and Control

Division of the David Taylor Model Basin who contributed to the investigation described by this report. Particular thanks are due to Mr. Samuel H. Brooks

who was responsible for the adaptation of the test equipment and the preparation

of the model for tests, to Mr Erich H Dittrich who was responsible for

con-ducting the tests in the Rotating Arm and Straightline Basin Facilities, and to Mr. Nan King who assisted in the reduction and analysis of the data contained

in this report.

REFERENCES

" Maneuverability Committee Report," Proceedings of the Tenth Inter-national Towing Tank Conference, Volume 1 (September 1963).

Morse, R. V. and Price, D., "Maneuvering Characteristics of the

MARINER Type Ship (USS COMPASS ISLAND) in Calm Seas," Sperry Gyroscope Publication G7-22.33- 1019 prepared for David Taylor Model Basin under Contract Nonr 306 1(00) (December 1961).

"Maneuverability Committee Report, Appendix 1, !'Proceedings of the Eleventh International Towing Tank Conference (October 1966).

"Maneuverability Comthittee Report, Appendix 2," Proceedings of the Eleventh International Towing 'lank Conference (October 1966).

Russo, V. L. and Sullivan, E. K., "Design of the MARINER Type Ship, Transactions of the Society of Naval Architects and Marine Engineers, Volume 61 (1953).

Brownell, W. H., Two New Hydromechanics Research Facilities at David Taylor Model Basin," David Taylor Model Basin Report 1690 (December 1962).

"Research Facilities at the David Taylor Model Basin," David Taylor Model Basin Report 1913 (October 1960).

8 Gertler, Morton, "The DTMB Planar-Motion-Mechanism System,"

Proceedings of Symposium on Towing Tank Facilities, Instrumentation and Measuring Techniques, Zagreb, Yugoslavia (September 1959).

APPENDIX A

HYDRODYNAMIC DATA OBTAINED FROM

ROTATING-ARM TESTS

(Tables 6 through 9 and Figures 1.5 through 20)

TABLE 6

Data from Rotating-Arm Tests for 20-Knot Condition

(F = 0. 259, J U = 0. 979)

nD

(Value, for Coefficiente X'.'Y', and Nmu.t be multiplied by lOs)

36 degrees degrees6R X' Y' N' 0.2045 0.0

.0.0

-0.135 0.379 -0.530 1.0 -0.169 0.706 -0.487 2.0 -0.186 1.009 -0.427 3.0 -0.197 1.325 -0.377 4.0 -0.220 1.725 -0.335 5.0 -0.346 1.990 -0.305 6.0 -0.259 2.253 -0.282 8.0 -0.368 3.306 -0.251 10.0 -0.582 '4.120 -0.149 12.0 -0. 599 4.896 -0. 070 15.0 -0.724 6.101 0.069 18.0 -0.742 7.599 0.314 -5.0 -0.116 -1.057 -1.024 0.2045 0.0 0.0 -0.124 0.400 -0.507 0.2045 0.0 -5.1 ' 0.165 -0.400 0.0 -0. 087 0.460 -0. 509 5.0 -0. 101 0.603 -0. 669 -2.0 -0. 157 0.334 -0. 470 -4.0 -6.0 ..0.101-0. 10,1 ' 0.250 0. 180 -0.420-0. 383 -7.9 -0. 016 -0. 362 -10.0 -0.093 -0.343 -15.0 -0.240 ' -0.167 -20.0 ' ' -0.407 -0.046 0.2045 0.0 -25.0 -30.0 -35.0 ., ' ' -0.468 -0.538 -0.554 0.049 0.093 0,080

TABLE 6 (Con't)

Data f-rom Rotafing-Arm. Tests for 20-Knot ConditiOn.

(F=

U

=0.259. 3=

=0979)

nD

(Values for Coefficients .X. V, arid N must be multiplied by lO-)

37 $ degrees degrees X' Y' N' 0.1858 0.0 0..0

-o106

0.423 -0.463 0.1982 -0.129 0.387 . 0.527 0.2045 -0.129 0.371 -0.543 0.2112 -0.092 0.415 -0.551 2274. I -0. 087 0.503 -0.600 0.2462 -0.092 0.513 -0,655 0 2667 -0 083 0 593 0 690 O.2930 -0.083 0.645 -0.778 0.3249 . -0.069 0.653 -0.892 0.3616 . 0.0

0858

L0i5

0.4398 0.028 L068 -1.277 0.5164 . 0.016 1.357 -1.577 0.6246 0.092 1,758 -1.976 0.7757 0.0 0..0 -0.002 2.305 -2. 743 0.6246 20.0 0 -1.182 13.916 -2.733 15 0 =0. 912 10. 215 -2. 420 10.0 . -0.661 6.990 -21.135 5.0 -0.269 3.860 -1.884 0.6246 -5.0 0 0.232 =1.201 -2.337 0.6246 0.0 -5.0 0.175 1.463 -1.86.5 -10.0 0Q88 1.116 -1.739 -15,0 . 0.078 0.792 -L615 =20.0 0.0Z8 0.815 -1.457 -24.8 .0.115 0.727 -1.365 -25.0 0.097 0.553 -1.400 -30.0 -0.226 0.374 -1.295. -35 0 -0 272 0 301 -1 219 0.6246 0.0

-204

-0.005 0.748 1.441

TABLE 6 (Con't)

Data from Rotating-Arm Tests for 20-Knot Condition

(F = 0. 259, J = = 0.979)

nD

(Valueo for, Coefficienta X' Y- and N' muat be multiplied by lOs)

38 degrees degrees X' Y' N' 0.6246 10.0 -5.0 -0.491 7.096 -1.983 -10.0 -0.541 6.817 -1.808 -15.0 -0.60.1 6.364 -1.669 -20.3 -0.689 5.943 -1.470 -25.0 -0.823 5.570 -1.311 -30.0 -0.864 6.001 -1.181 -34.9 -0.989 5.435 -1.167 -30.0 -1.035 5.679 -1.232 0.6246 10.0 -10.0 . -0.712 6.475 -1.770 0.6246 ' 20.0 ' -5.0 -1.237 13.912 -2.610 -10.0 -1.408 13. 802 -2.448 -15.0 -1.279 12.593 -2.239 -20.0 -1.509 12.943 -2.090 -25.0 -.1.583 12.190 -1.881 -30.0 -1.684 12.636 -1.732 -35.0 -1.813 12.309 -.1.739 0.6246 20.0 -15.0 -1.389 13.292 -2.271 0.2930. 20.0 0.0 -0.709 8.952 -0.196 15.0 -0.747 6.587 -0.434 10.0 . . -0.503 4.396 -0.535 5.0 -0. 202 2. 199 -0. 608 -5.0 0.092 -0.996 -1.387 15.0 . . -0.742 6.618 -0.456 0.2930 ' 20.0 0.0 -0.875 9.168 -0.171 0.2930 0.0 -5.0 -10.0 -0. 046 , -0.074 -0. 007-0. 172 -0. 731-0.617 -15.0 -0. 101 -0. 222 -0. 479 -20.0 -0. 217 -0. 232 -0. 302 -25.0 -0. 277 -0. 329 -0. 193 -30.0 -0. 410 -0. 354 -0. 139 0.2930: 0.0 -35.0 -0.493 0. 418 -0. 139

TABLE 6 (Con't)

Data from Rotating -Arm Tests for 20-Knot Condition

IT

(F = 0. 259, 3 = 0. 979)

(Valuec for Coefficiente X.Y and.N niugt be multiplied by

39 degrees degrees6R X' Y' N' 0.2930 10.0 .0.0 -0. 083 4.482 -0. 532 -5.0 -0.475 4.114 . -0.366 -10.0 -0. 503 3.813 -0. 212 -15.0 -0.609 3.596 -0.082 -20.0 -0.743 3.368 0.049 -25.0 -0.909 3.871 0.220 -30.0 -0.950 3.343 0.205 -35.0 -1.075 3.518 0.317 -25.0 -0.872 3.654 0.195 -10.0 -0. 549 3.836 -0. 232 -30.0 -0. 959 3. 575 0. 241 0.2930 10.0 -35.0 -1.042

3547

0.305 0. 2930 20.0 -5.0 -0. 75 8.828 -0. 016 -10.0 -0.805 .8.624 0.120 -1.5.0 -0.842 8.317 0.298 -20.0 -0.934 8.224 0.472 -25.0 -1.050 7.774 0.580 -30.0 -1.119 7.850 0.684 -35.0 -1.257 7.605 0.703 -25.0 -1.064 7.743 0.586 -30.0 -1.165 7.605 0.637 -20.0 -1.479 7.882 0.42,1 .0.0 -0.884 9.019 -0.186 -35.0 -1.276 7.767 0.766 0.2930 20.0 -20.0 -0. 902 8.059 0.476 0.2045 0.0 -10.0 -0.129 -0.257 -0.349 -15.0 -0. 198 -0. 232 -0..168 -20.0 -0.240 -0.459 -0.046

25O

-0.. 318 -0. 587 0. 048 -35.0.. -0.516 -0.642 0.072 -20.0 -0.249 -0.422 0.050 0.2045 0.0 -15.0 -0.189 -0.249 -0.167

TABLE 6(Con't)

atá from Rota.ng-Arm.Tests for 20-Knot Condition

(F = 0. 259, J = 0. 979)

nD

(Valuee for Coefficiente X'.-Y',-and N muet be multiplied by lOs)

40 P degrees 6 degrees V .. Nt 0.. 2045 10.0 0.0 -O 465. 3. 723 -0. 141 -5.0 -0.501 3.478 0.008 -10.0 -0.525 3.196 0.143 -15.0 -0.654 3.354 0.301 -20.0 -0.741 3.113 _0.444 -25.0 -0.833 2.963 0.541 -30.0 -0.875 2.851 0.609 -34.9 -0.963 2.842 0.667 -35.0 . -0.:967 2.688 0.678 -5.0 -0.478 3.506 0.012 -.15.0. -0.649 .3.293 0.308 0.2045 10.0 -15.0 -0.626 3.453 0.328 0.2045

:20.0

0.0 -0.740 8.281 0.490 -5.0 -0.768 8.074 0.595 -35.0 -1.247 7.47.5 1.354 -10.0 -0.768 7.923 0. 747 -15.0. -0.883 8.068 0. 953 -25.0 . -1.044 7.645 1.261 -30.0 -1.095 7.675 1.382 -35.0 . -1.187 7.728. 1.442 -20.0 -0.94? 7.817 1.135 -20.0 -0.961 7.836 1.076 -15.0 -0.887 7.743 0.879 -30.0 -1.155 7.715 1.324 0.2045 20.0 -35.0 -1.275 7.966 1.437

TABLE 7

Data from Rotating-Arm Tests for 10-Knot Condition

(F= ti

= 0.1295, J=

.IgL

# F F

(Value, for Coefficient, X Y and N must be multiplied by 10 ₎

41 = 0.979) nD rt _$ deg deg Yt IP 0.2045 -5.0 0.0 -0. 132 -0.774 -0.768 0; 0 -0. 202 0. 262 _{-0. 450} +5.0 _{-0.309 1.812 -0.232} 10.0 -0.508 3.452 -0.136 15.0 -0.618 5.244 -0.111 0.2045 20.0 0.0 -0.768 7.886 -0.101 0. 2045 0.0 0.0 -0.184 0.428 -0.432 -5. 0 -0. 184 0. 170 -0. 321 -10.0 -0.221 0.115 -0.157 -15. 0 -0. 294 -0. 106 -0. 076 -20.0 -0. 331 -0. 345 0.018 -25.0 -0. 515 -0. 418 0.063 -30.0 -0.496 -0.455 0.093 -35.0 -0.588 -0.326 0.157 -35.0 -0. 625 -0. 547 0. 131 -30.0 -0.460 -0.492 0.129 -25.0 -0.441 -0.400 0.076 -20.0 -0.349 -0.291 0.030 -15.0 -0.257 -0.193 -0.051 -10.0 -0.202 0.005 -0.167 -5.0 -0. 129 0.060 -0. 311 0.2045 0.0 0.0 -0.110 0.372 -0.445 0.2045 10.0 0.0 -0.563 3.451 -0.144 -5.0 -0.361 3.250 0.008 -10.0 -0.380 3.013 0.152 -15.0 -0.471 2.942 0.303 -20. 0 -0.766 2.723 0. 427 -25.0 -0. 858 2.496 0. 553 -30. 0 -0. 876 2. 362 0. 619 0.2045 10.0 -35.0 -1.005 2.189 0.639

TABLE 7 (Cont)

Data from Rotating-Arm Tests for 10-Knot Condition

(F = = 0. 1295, J = = 0.979)

(Velueo for Coefficienta X'.Y'.' and N muat be multiplied by lOs)

42

r'

deg 'deg8R Y' N' 0.2045 20.0 0.0 -0.529 7.886 -0.144 -5.0 -0.474 7.595 0.035 -10.0 -0. 603 7. 286 0. 192 -15.0 -0.584 6.819 0.369 -19.9 -0.676 6.545 0.515 -25.0 -0.805 6.345 0.662

-300

-0.897 6.519 0.765

-35.0.

-1.025 6.530 0.841 -35.0 -1.246 6.357 0.780 -30.0 -1.117 6.603 0.735 -25.0 -1.007 6.439 0.647. -20.0 -0.897 6.633 0.493 -15. 0 -0. 860 6.838 0. 374 -10.0 -0.786 7.159 0.205 -5.0 -0. 676 7.556 0.063 0.2045 20.0 0.0 -0.639 8.019 -0.124 0.6246 -5.0 0.0 0.240 0.279 -1.980 -5.0 0.295 0.298 -1.773 -10.0 0 -0. 144 -1. 662 -15.0 0.171 -1.546 -20.0 -0.018 -0.769 -1.384 -25.0 0.074 -0.511 -1.288 -30.0 -1.273 -1.202 -35.1 _{-0.849 -1.243} -30.0 0.220 -1.735 -1.273 0.6246 -5.0 -35.0 -0.165 -1.177 0. 6246 0. 0 0. 0 -0. 055 2. 026 -1. 743 -5.0 -0.055 -1.586 -10.0 _-0.129 1.477 -1.520 -15.0 -0.165 2.056 -1.313 -20.0 =0. 202 1.007 -1.217 -25.0 -0.257 0.808 -1.015 -30.0 -0. 368 1. 175 -0. 889 -35.0 -0. 460 0.375 -0. 914 -5.0 -0.037 1.504 -1.611